Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

We analyze three one parameter families of approximations and show that they are symplectic in Lagrangian sence and can be related to symplectic schemes in Hamiltonian sense by different symplectic ...

Inspired by path integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids ...